A differential game analysis of firms' Greentech innovation with emission tax in oligopoly exhibiting network externality

Abstract In the practice of Greentech innovation, there are two distinct paths: the first is replacement technology innovation, aimed at improving replacement technology, and the second is end‐of‐pipe technology innovation, aimed at reducing end‐of‐pipe emissions. This paper examines Greentech innovation and emission taxation in an oligopoly market with network externality. Its key features include (i) extending the literature on classical Greentech innovation by modeling it as a dynamic oligopoly with network externality; (ii) incorporating an inverse demand function that depends on output levels and network value; and (iii) imposing emission taxes on emissions rather than environmental damage. The main findings are (i) a saddle‐point steady‐state equilibrium exists under both firm and social planner decisions; (ii) an increase in efforts for replacement technology innovation leads to higher output and prices, whereas an increase in efforts for end‐of‐pipe technology innovation leads to lower output and higher prices; (iii) emissions increase (decrease) with increased efforts for replacement technology innovation when the network size is large (small), while emissions consistently decrease with increased efforts for end‐of‐pipe technology innovation, regardless of network size; (iv) in the steady‐state equilibrium, the social planner can achieve full Greentech adoption by either setting an appropriate tax rate (for a given number of firms) or regulating market access (for a given tax rate). Additional insights are presented through propositions and conclusions. This study complements and advances the classical economies of scale approach to Greentech innovation by shifting the focus from production‐side to demand‐side dynamics.